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1

$begingroup$

Motivation:

The (principal) value of

$$mpmodn$$

for some positive integers $m> n$, might well be viewed as the value

$$m-sum_i=1^M_m,nn,tag$Sigma$$$

for some $M_m,nin Bbb N$ with $M_m,nnle m$ but $(M_m,n+1)n> m$; indeed, we have just subtracted a suitable number $M_m,n$, dependent of $n$ and $m$, of $n$s from $m$.

The Questions:

What happens if we replaced our fixed $n$ by a sequence $(a_n)in Bbb N^Bbb N$, so that, for instance, for small $m$, where the threshold $M_m, (a_n)$ is also low, one substacts only a handful of terms? Has such a thing been studied before and, if so, what is its name? What properties does it have?

Example:

Consider the natural numbers $(n_n)inBbb N^Bbb N$ (of which $0$ is not a member). Then, say,

$$beginalign
7pmod(n_n)&=7-sum_n=1^M_7, (n_n)n \
&=7-fracM_7, (n_n)2(M_7, (n_n)+1)\
&=1,
endalign$$

since $M_7, (n_n)=3$ here.

---

I like how a sequence $(M_m, (a_n))_min(Bbb Ncup0)^Bbb N$ is generated.

Please help :)

sequences-and-series elementary-number-theory modular-arithmetic terminology definition

share|cite|improve this question

asked Feb 27 at 23:36

ShaunShaun

9,334113684

$endgroup$

This question has an open bounty worth +50
reputation from Shaun ending ending at 2019-03-15 20:48:18Z">in 6 days.

This question has not received enough attention.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I understand your definitions but I don't understand the point of your question. What kind of "properties" are you exepcting to find ?
  $endgroup$
  – Ewan Delanoy
  13 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @EwanDelanoy: The point? To help satisfy my curiosity on the matter. What am I expecting to find? I don't know, something like the fact that if $(a)ina^Bbb N$, then $$mpmod(a)=mpmoda$$ for $ainBbb N$.
  $endgroup$
  – Shaun
  12 hours ago
  

  
  
  
  

add a comment | 

1

$begingroup$

Motivation:

The (principal) value of

$$mpmodn$$

for some positive integers $m> n$, might well be viewed as the value

$$m-sum_i=1^M_m,nn,tag$Sigma$$$

for some $M_m,nin Bbb N$ with $M_m,nnle m$ but $(M_m,n+1)n> m$; indeed, we have just subtracted a suitable number $M_m,n$, dependent of $n$ and $m$, of $n$s from $m$.

The Questions:

What happens if we replaced our fixed $n$ by a sequence $(a_n)in Bbb N^Bbb N$, so that, for instance, for small $m$, where the threshold $M_m, (a_n)$ is also low, one substacts only a handful of terms? Has such a thing been studied before and, if so, what is its name? What properties does it have?

Example:

Consider the natural numbers $(n_n)inBbb N^Bbb N$ (of which $0$ is not a member). Then, say,

$$beginalign
7pmod(n_n)&=7-sum_n=1^M_7, (n_n)n \
&=7-fracM_7, (n_n)2(M_7, (n_n)+1)\
&=1,
endalign$$

since $M_7, (n_n)=3$ here.

---

I like how a sequence $(M_m, (a_n))_min(Bbb Ncup0)^Bbb N$ is generated.

Please help :)

sequences-and-series elementary-number-theory modular-arithmetic terminology definition

share|cite|improve this question

asked Feb 27 at 23:36

ShaunShaun

9,334113684

$endgroup$

This question has an open bounty worth +50
reputation from Shaun ending ending at 2019-03-15 20:48:18Z">in 6 days.

This question has not received enough attention.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I understand your definitions but I don't understand the point of your question. What kind of "properties" are you exepcting to find ?
  $endgroup$
  – Ewan Delanoy
  13 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @EwanDelanoy: The point? To help satisfy my curiosity on the matter. What am I expecting to find? I don't know, something like the fact that if $(a)ina^Bbb N$, then $$mpmod(a)=mpmoda$$ for $ainBbb N$.
  $endgroup$
  – Shaun
  12 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

Motivation:

The (principal) value of

$$mpmodn$$

for some positive integers $m> n$, might well be viewed as the value

$$m-sum_i=1^M_m,nn,tag$Sigma$$$

for some $M_m,nin Bbb N$ with $M_m,nnle m$ but $(M_m,n+1)n> m$; indeed, we have just subtracted a suitable number $M_m,n$, dependent of $n$ and $m$, of $n$s from $m$.

The Questions:

What happens if we replaced our fixed $n$ by a sequence $(a_n)in Bbb N^Bbb N$, so that, for instance, for small $m$, where the threshold $M_m, (a_n)$ is also low, one substacts only a handful of terms? Has such a thing been studied before and, if so, what is its name? What properties does it have?

Example:

Consider the natural numbers $(n_n)inBbb N^Bbb N$ (of which $0$ is not a member). Then, say,

$$beginalign
7pmod(n_n)&=7-sum_n=1^M_7, (n_n)n \
&=7-fracM_7, (n_n)2(M_7, (n_n)+1)\
&=1,
endalign$$

since $M_7, (n_n)=3$ here.

---

I like how a sequence $(M_m, (a_n))_min(Bbb Ncup0)^Bbb N$ is generated.

Please help :)

sequences-and-series elementary-number-theory modular-arithmetic terminology definition

share|cite|improve this question

asked Feb 27 at 23:36

ShaunShaun

9,334113684

$endgroup$

share|cite|improve this question

asked Feb 27 at 23:36

ShaunShaun

9,334113684

share|cite|improve this question

asked Feb 27 at 23:36

ShaunShaun

9,334113684

asked Feb 27 at 23:36

ShaunShaun

9,334113684

asked Feb 27 at 23:36

ShaunShaun

9,334113684